Author: Dann Corbit
Date: 13:46:21 12/11/02
Go up one level in this thread
On December 11, 2002 at 15:04:41, J. Wesley Cleveland wrote: >On December 10, 2002 at 18:28:08, Dann Corbit wrote: > >>On December 10, 2002 at 18:24:20, Uri Blass wrote: >> >>>On December 10, 2002 at 18:12:53, Dann Corbit wrote: >>> >>>>On December 10, 2002 at 17:55:51, Dann Corbit wrote: >>>> >>>>>On December 10, 2002 at 17:51:40, Ingo Lindam wrote: >>>>> >>>>>>On December 10, 2002 at 17:30:47, Dann Corbit wrote: >>>>>> >>>>>>>On December 10, 2002 at 13:42:36, Bernardo Wesler wrote: >>>>>>>[snip] >>>>>>>>THE ALGORITHM. A MATHEMATICAL FORMULA THAT , FOR EXAMPLE, ASSURE YOU THAT IF YOU >>>>>>>>DO THE FIRST MOVE YOU ALWAYS WIN. >>>>>>>>I MEAN TO THINK ABOUT DISCOVERING A CHESS ALGORITHM IS AN UTHOPY? >>>>>>> >>>>>>>Provably impossible on current hardware and software systems. >>>>>>>Maybe in 100 years the game will be formally solved. Not in the near futre. >>>>>> >>>>>>provably impossible on current hardware...? >>>>>>are you sure? >>>>> >>>>>Absolutely sure. >>>>> >>>>>To solve chess you must store at least the square root of nodes of the solution >>>>>tree. Considering the half move clock and castle rights, it easily exhausts any >>>>>possibility of solution. >>>>> >>>>>>without assuming anything about the kind of solution? >>>>> >>>>>No assumptions are necessary. We pick an adversary in the tree. It's just like >>>>>how you would prove a sort works in O(f(n)). >>>>> >>>>>>atleast you are assuming the use of hardware... >>>>>>(an assumtion I could live with because I wouldn't bet on find the solution >>>>>>faster by using just a pencil and a sheet of paper :-)) >>>>> >>>>>I am assuming that if you turned the universe into silicon chips and devoted >>>>>half of them to CPU's and the other half to memory storage that all the stars >>>>>will go out before you find the answer. >>>>> >>>>>>me would like to see the proof for 'provably impossible' as much as I would like >>>>>>to see the solution for chess >>>> >>>>10^48 formations * 100 states for half-move clock * 4 bits for castle state. >>>>sqrt(1.5e+51) = 38729833462074168851792654 [64 moles of positions ;-)] >>> >>>Most of the legal positions are irrelvant for solving chess because they can >>>happen only after both sides play illogical moves. >> >>They are still fully relevant. You might throw away your queen and both rooks >>and still win (in fact, it has been done). >> >>>I do not know the number of legal positions but I know no proof that there are >>>more than 10^40 and I know no proof that the relevant legal positions to solve >>>chess are more than 10^20 >>> >>>positions like 1.a4 a6 may be irrelevant to solve chess if you find that 1.a4 is >>>losing against 1...e5 when 1.e4 is not losing. >> >>In order to prove that they are irrelevant, you will have to solve the tree. In >>order to solve the tree you will have to compute and store it. > >Except he does not have to prove that they are irrelevant, you have to prove >they are relevant. If he has not disproven them, then he has not demonstrated his point of a suggested outcome. Either I am not communicating clearly or you do not understand what I have said. >>>in that case knowing the theoretic result after 1.a4 a6 is going to change >>>nothing. >>> >>>Tree is only one way to prove things. >>> >>>It is possible to prove that KQ vs K without the 50 move rule win in n*n chess >>>board for every dimension n. >> >>Believe it or not, you form a tree to solve it. You might have an alternate >>formulation, but a tree solution will be perfectly equivalent and optimal. > >You are wrong here. You can prove by induction that KQ vs K is mate on a >chessbord that is e.g. 10^17 by 10^17, while the tree is roughly the same size >as the tree of chess. How many moves will the induction contain? The same as the tree.
This page took 0.01 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.